L.S., > If I have N pools of entropy (all same size X) and I pool them > together with XOR, is that as good as it gets? > > My assumptions are: > > * I trust no single source of Random Numbers. > * I trust at least one source of all the sources. > * no particular difficulty with lossy combination. I take the last item to mean that you do not mind wasting entropy but want to be sure the resulting random number is unpredictable.

If you add one additional assumption: * The sources are independent of each other then the XOR of the random sources will be at least as unpredictable as the most unpredictable individual random source (to keep away from the entropy discussion). As far as I can se, this the "if at least one source is unpredictable for a workload of x, the resulting random is also at least that unpredictable" property that you seem to be looking for. If the sources are not independent, in the most extreme case: the sources are the same, the result is not so good. XORing in the same RNG stream twice, however good the RNG, is not so useful ;-) Without the threatmodel, I am not sure if this is a problem for you, but if the attacker has control or knowledge of some of the sources, he also knows the XOR of the remaining ones. In the case he knows all but one sources, and the remaining source is not so unpredictable (LFSR, poorly biased noise source), the result can be quite predictable (and in weak RNG designs, the remaining source might be compromised). Note that this could also be used to force the combined RNG to more likely generate a chosen output. Using hashfunctions to combine the randoms makes it computationally harder for such chosen results to be generated, it quickly becomes effectively a search problem for hash-collisions where you have only limited choice on the input. Also temporary lulls in the quality of the random sources are much better handled. Peter Gutmann's dissertation has a very good description of what he did for hardening his cryptolib's the random generation from many such attacks/mistakes. With kind regards, Wouter Slegers --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to [EMAIL PROTECTED]